Question

Evaluate
$(\sin A+\cos A)(\tan A+\cot A)$

• A. $\sin A+\cos A$
• B. $\sec A+cosecA$
• C. $\sin A$
• D. $\cos A$

Answer 1

The correct option is B $\sec A+cosecA$

The value of $(\sin A+\cos A)(\tan A+\cot A)$ is
$=(\sin A+\cos A)(\frac{\sin A}{\cos A}+\frac{\cos A}{\sin A})$
$=(\sin A+\cos A)\left(\frac{{\sin }^{2}A+{\cos }^{2}A}{\cos A\sin A}\right)$
$=\frac{\sin A+\cos A}{\cos A\sin A}$
$=\frac{\sin A}{\cos A\sin A}+\frac{\cos A}{\cos A\sin A}$
$=\frac{1}{\cos A}+\frac{1}{\sin A}$

$=\sec A+cosecA$